TON DUC THANG UNIVERSITY
FACULTY OF ELECTRICAL AND
ELECTRONICS ENGINEERING
401065
ELECTRIC MACHINES
CHAPTER 1:
MAGNETIC CIRCUIT, PRINCIPLES
OF ELECTROMECHANICAL ENERGY
CONVERSION
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401065 - Chapter 1: Magnetic Circuit, Principles
Of Electromechanical Energy Conversion
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CHAPTER 1: MAGNETIC CIRCUIT,
PRINCIPLES OF ELECTROMECHANICAL
ENERGY CONVERSION.
1.1. Magnetic field and magnetic circuits
1.2. Properties of magnetic materials
1.3. Basic electromagnetic laws of electric
machines
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401065 - Chapter 1: Magnetic Circuit, Principles
Of Electromechanical Energy Conversion
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OBJECTIVES
➢ Understand the magnetic field and
magnetic circuit
➢ Understand the properties of magnetic
materials
➢ Understand some basic electromagnetic
laws
➢ Calculate a simple magnetic circuit
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1.1. MAGNETIC FIELD AND
MAGNETIC CIRCUITS
1.1.1. Magnetic field
Magnetic fields are the fundamental mechanism by
which energy is converted from one form to another
in motors, generators and transformers.
➢ The Ampere’s Law : A current-carrying wire
produces a magnetic field in the area around it.
 H.dl =  I
C
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Of Electromechanical Energy Conversion
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1.1. MAGNETIC FIELD AND
MAGNETIC CIRCUITS
1.1.1. Magnetic field
➢ Consider a current carrying conductor is
wrapped around a ferromagnetic core:
The Ampere’s Law becomes:
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H. lc = N. i
401065 - Chapter 1: Magnetic Circuit, Principles
Of Electromechanical Energy Conversion
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1.1. MAGNETIC FIELD AND
MAGNETIC CIRCUITS
1.1.1. Magnetic field
H. lc = N. i
H : magnetic field intensity
(ampere-turns per meter) is
known as the effort required to
induce a magnetic field.
B = . H
• B : magnetic flux density [Wb/m2 or T – Tesla]
• µ= r.0 : magnetic permeability of material [Henrys per meter – H/m]
• r =  / 0 : relative permeability of material
• 0= 4.10-7: magnetic permeability of free space
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1.1. MAGNETIC FIELD AND
MAGNETIC CIRCUITS
1.1.1. Magnetic field
B = .H =
 . N .i
➢ In a core such as figure:
lc
➢ The total flux flowing in the ferromagnetic core,
consideration has to be made in terms of its cross
sectional area (CSA). Therefore:
 =  B.dAc = B. Ac
Ac
Where : Ac - cross sectional area throughout the core (m2)
or :
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=
 . N .i. Ac
lc
 [Weber – Wb]
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Of Electromechanical Energy Conversion
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1.1. MAGNETIC FIELD AND
MAGNETIC CIRCUITS
1.1.2. Magnetic circuits
N .i = H .lc
 N .i = B .lc

 N .i =   1  lc
 A
  c
 1  lc
 F = N .i =    =  .R
   Ac
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F : magnetomotive force (mmf)
R : reluctance
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Of Electromechanical Energy Conversion
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1.1. MAGNETIC FIELD AND
MAGNETIC CIRCUITS
1.1.2. Magnetic circuits
➢ The flow of magnetic flux induced in the
ferromagnetic core can be made analogous to an
electrical circuit hence the name magnetic circuit.

I
+
E
(emf)
R
Electric Circuit Analogy
F=Ni
(mmf)
+
-
Reluctance, R
Magnetic Circuit Analogy
F = N. I = . R (similar E = I. R)
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401065 - Chapter 1: Magnetic Circuit, Principles
Of Electromechanical Energy Conversion
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1.1. MAGNETIC FIELD AND
MAGNETIC CIRCUITS
1.1.2. Magnetic circuits
➢ The polarity of the mmf will determine the
direction of flux by apply the ‘right hand curl’ rule:
▪ The direction of the curled fingers determines the
current flow.
▪ The resulting thumb direction will show the magnetic
flux flow.
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1.1. MAGNETIC FIELD AND
MAGNETIC CIRCUITS
1.1.2. Magnetic circuits
➢ Consider a magnetic circuits with a air gap as figure:

Rc
F=N.i
Rg
Bc =

Ac
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Bg =

Ag
F = H c .lc + H g . g =
Bc

401065 - Chapter 1: Magnetic Circuit, Principles
Of Electromechanical Energy Conversion
.lc +
Bg
0
.g
11
1.1. MAGNETIC FIELD AND
MAGNETIC CIRCUITS
1.1.2. Magnetic circuits
➢ Consider a magnetic circuits with a air gap as figure:

Rc
F=N.i
Rg
lc
Rc =
 . Ac
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g
Rg =
0 . Ag
F =  (Rc + Rg )
401065 - Chapter 1: Magnetic Circuit, Principles
Of Electromechanical Energy Conversion
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1.1. MAGNETIC FIELD AND
MAGNETIC CIRCUITS
1.1.2. Magnetic circuits
I

R1
V
Rc
F=N.i
Rg
R2
Electric Circuit Analogy
V
I=
R1 + R2
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Magnetic Circuit Analogy
F
F
=
=
(Rc + Rg )  lc   g 

 +
  .A 

.
A
c 

 0 g
401065 - Chapter 1: Magnetic Circuit, Principles
Of Electromechanical Energy Conversion
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1.1. MAGNETIC FIELD AND
MAGNETIC CIRCUITS
1.1.2. Magnetic circuits
➢ In general, magnetic circuits can consist of
multiple elements in series and parallel:
Example 1.1
 H  =  (R  ) = (N i ) = F = F
m
m
j
j =1
j
n
j
j =1
n
j k
k =1
k
k =1
H1l1 - H2l2 = (R1 + R2) = N1i1 – N2i2 = F1– F2
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1.1. MAGNETIC FIELD AND
MAGNETIC CIRCUITS
1.1.2. Magnetic circuits
Example 1.2: A magnetic
circuit with a single air gap
is shown in Fig. the
relative permeability of the
core is 4000 H/m. Given
this information, find:
a/ The total reluctance of
the flux (iron plus air gap)
path
b/ The current required
to produce a flux density
of 0.5T in the air gap
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1.2. PROPERTIES OF MAGNETIC
MATERIALS
1.2.1. The magnetization curve B-H
➢ In the non-magnetic materials, they have
constant permeability. (Ex: the permeability of
free space is 0= 4.10-7 (H/m))
➢ The permeability of magnetic materials is much
higher than µ0.
➢ However, the permeability is not linear anymore
but does depend on the current over a wide
range.
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1.2. PROPERTIES OF MAGNETIC
MATERIALS
1.2.1. The magnetization curve B-H
➢ The concept of magnetic permeability r
corresponds to the ability of the material to
permit the flow of magnetic flux through it.
➢ In electrical machines, linear relationship
between B and I is desired, which is normally
approached by limiting the current.
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401065 - Chapter 1: Magnetic Circuit, Principles
Of Electromechanical Energy Conversion
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1.2. PROPERTIES OF MAGNETIC
MATERIALS
1.2.1. The magnetization curve B-H
➢ Look at the magnetization curve and B-H curve.
 (Wb)
B (T)
F (A.turns)
H (A.turns/m)
The curve corresponds to an increase of DC current flow through a coil
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1.2. PROPERTIES OF MAGNETIC
MATERIALS
1.2.2. Energy losses in a ferromagnetic
core
➢Hysteresis Loss
Typical Hysteresis loop when AC current is applied.
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1.2. PROPERTIES OF MAGNETIC
MATERIALS
1.2.2. Energy losses in a ferromagnetic
core
➢Eddy Current Loss
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1.2. PROPERTIES OF MAGNETIC
MATERIALS
1.2.2. Energy losses in a ferromagnetic
core
➢Conclusion:
Core loss is extremely important in practice, since it
greatly affects operating temperatures, efficiencies, and
ratings of magnetic devices.
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1.3. BASIC ELECTROMAGNETIC
LAWS OF ELECTRIC MACHINES
1.3.1. Faraday’s law - Induced voltage from
a time-changing magnetic field
“If a flux passes through a turn of a coil of wire, voltage will be
induced in the turn of the wire that is directly proportional to the
rate of change in the flux with respect of time”
d
ei = −
dt
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1.3. BASIC ELECTROMAGNETIC
LAWS OF ELECTRIC MACHINES
1.3.1. Faraday’s law - Induced voltage from
a time-changing magnetic field
➢ If there is N number of turns in the coil with the
same amount of flux flowing through it, hence:
d
d
eind = − N
=−
= − N .ei
dt
dt
where  (flux linkage) is defined as:  =
N
  (Wb-turn)
i =1
i
Faraday’s law is the fundamental property of
magnetic fields involved in transformer operation.
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1.3. BASIC ELECTROMAGNETIC
LAWS OF ELECTRIC MACHINES
1.3.2. Faraday’s law - Induced voltage on a
conductor moving in a magnetic field
“If a conductor moves or ‘cuts’ through a
magnetic field, voltage will be induced
between the terminals of the conductor”
eind = (v  B) l  sin
v (m/s) – velocity of the wire
B (T) – magnetic field density
l (m)– length of the wire in the magnetic field
 - angle between v and B
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1.3. BASIC ELECTROMAGNETIC
LAWS OF ELECTRIC MACHINES
1.3.2. Faraday’s law - Induced voltage on a
conductor moving in a magnetic field
The induction of voltages in a wire moving in a
magnetic field is fundamental to the operation of all
types of generators.
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1.3. BASIC ELECTROMAGNETIC
LAWS OF ELECTRIC MACHINES
1.3.3. Electromagnetic force action to a
current carrying conductor in a magnetic
field
“When a current-carrying conductor is
placed in a magnetic field, it is subjected to
a force which we call electromagnetic
force. The magnitude of the force depends
upon the orientation of the conductor with
respect to the direction of the field”
F = i B l sin
F(N); B(T); l (m); i(A)
 - angle between i and B
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1.3. BASIC ELECTROMAGNETIC
LAWS OF ELECTRIC MACHINES
1.3.3. Electromagnetic force action to a
current carrying conductor in a magnetic
field
This phenomenon is the basis of an electric motor
where torque or rotational force of the motor is the
effect of the stator magnetic field and the current of
the rotor
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SUMMARY AND ASSIGNMENT
➢ In this chapter, we have learnt:
▪ Basic concept of magnetic field and magnetic
circuit.
▪ Properties of magnetic materials
▪ Basic electromagnetic laws of electric
machines
➢ ASSIGNMENTS:
▪ Refer: [1]: 2-42; [5]: 111-121
▪ Do the exercises in the next slides
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EXERCISES
EXERCISE 1
Figure shows a simplified rotor
and stator for a DC motor. The
mean path length of the stator is
50cm, and its csa is 12cm2. The
mean path length of the rotor is 5
cm, and its csa also may be
assumed to be 12cm2. Each air
gap between the rotor and the
stator is 0.05cm wide, and the csa
of each air gap (including fringing)
is 14cm2. The iron of the core has
a relative permeability of 2000,
and there are 200 turns of wire on
the core. If the current in the wire
is adjusted to be 1A, What will
the resulting flux density in the
air gaps be?
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EXERCISES
EXERCISE 2
The figure shows a conductor
moving with a velocity of 5m/s
to the right in the presence of
a magnetic field.
The flux
density is 0.5T into the page,
and the wire is 1m length,
oriented as shown. What are
the magnitude and polarity
of the resulting induced
voltage?
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EXERCISES
EXERCISE 3
The figure shows a wire
carrying a current in the
presence of a magnetic field.
The magnetic flux density is
0.25T, directed into the page. If
the wire is 1m long and carries
0.5A of current in the direction
from the top of the page to the
bottom.
What
are
the
magnitude and direction of
the force induced on the
wire?
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